"to convert into "color(blue)"trigonometric form"to convert into trigonometric form
"that is " x+yitor(costheta+isintheta)that is x+yi→r(cosθ+isinθ) where
color(red)(bar(ul(|color(white)(2/2)color(black)(r=sqrt(x^2+y^2))color(white)(2/2)|)))
"and " color(red)(bar(ul(|color(white)(2/2)color(black)(theta=tan^-1(y/x);-pi< theta<=pi)color(white)(2/2)|)))
"here " x=-3" and " y=-2
rArrr=sqrt((-3)^2+(-2)^2)=sqrt13
"now " -3-2i" is in the 3rd quadrant so must ensure that"
theta" is in the 3rd quadrant"
theta=tan^-1(2/3)=0.588larrcolor(red)" related acute angle"
rArrtheta=-pi+0.588~~-2.55larrcolor(red)" in 3rd quadrant"
rArr-3-2i=sqrt13(cos(-2.55)+isin(-2.55))
• color(orange)" Reminder" cos(-theta)=costheta ; sin(-theta)=-sintheta
rArr-3-2i=sqrt13(cos(2.55)-isin(2.55))
